preprint

Inserted: 2 may 2025
Last Updated: 2 may 2025

Year: 2025

Abstract:

We extend the theory of gradient flows beyond metric spaces by studying evolution variational inequalities (EVIs) driven by general cost functions $c$, including Bregman and entropic transport divergences. We establish several properties of the resulting flows, including stability and energy identities. Using novel notions of convexity related to costs $c$, we prove that EVI flows are the limit of splitting schemes, providing assumptions for both implicit and explicit iterations.

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• AFSS25.pdf